Combined Gas Law Calculator — P₁V₁/T₁ = P₂V₂/T₂

How it works

The combined gas law links the pressure, volume and absolute temperature of a fixed amount of gas across a change of conditions (LibreTexts):

P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂

It bundles together the three simpler gas laws — Boyle's (P and V), Charles's (V and T) and Gay-Lussac's (P and T) — into one relationship, useful whenever more than one condition changes at once. Rearranged to find the final volume:

V₂ = (P₁ × V₁ × T₂) ÷ (P₂ × T₁)

Two rules are essential. Temperature must be in kelvin (add 273.15 to °C), because the law uses absolute temperature — using Celsius gives wrong or impossible answers. And the pressure and volume units just need to match on both sides (atm with atm, L with L); they cancel. The amount of gas is assumed constant — no gas is added or removed.

The behavior is intuitive: raising the pressure squeezes the gas to a smaller volume, while raising the temperature expands it. When both change, the combined law balances the two effects.

Worked example

Take 10 L of gas at 1 atm and 300 K, then raise the pressure to 2 atm while keeping the temperature at 300 K:

V₂ = (1 × 10 × 300) ÷ (2 × 300) = 3000 ÷ 600 = 5 L

Doubling the pressure at constant temperature halved the volume — Boyle's law, as a special case. As a fuller example, 2.00 L at 308 K and 0.833 atm brought to STP (1 atm, 273 K) becomes 1.48 L.

Frequently asked questions

What is the combined gas law?

It is the relationship P₁V₁/T₁ = P₂V₂/T₂ for a fixed amount of gas. It combines Boyle's, Charles's and Gay-Lussac's laws so you can handle changes in pressure, volume and temperature together.

How do I solve for the final volume?

Rearrange to V₂ = (P₁ × V₁ × T₂) ÷ (P₂ × T₁). Enter the initial pressure, volume and temperature and the new pressure and temperature, with temperatures in kelvin.

Why must temperature be in kelvin?

The law uses absolute temperature, which starts at absolute zero. Celsius values can be zero or negative and would give nonsensical results, so convert to kelvin (K = °C + 273.15) first.

What units should pressure and volume be in?

Any, as long as they are consistent on both sides — atm with atm, kPa with kPa, litres with litres. The units cancel, so only the ratios matter.

How is this different from the ideal gas law?

The ideal gas law (PV = nRT) gives the absolute state of a gas at one set of conditions. The combined gas law compares two states of the *same* gas sample, so the amount and the constant R drop out.

What if the amount of gas changes?

Then the combined gas law no longer applies directly — you need the full ideal gas law, which includes the number of moles. The combined law assumes a fixed, sealed amount of gas.